1) Field of Invention
This invention relates to an acoustic resonator in which near-linear macrosonic waves are generated in a resonant acoustic chamber, having specific applications to resonant acoustic compressors.
2) Description of Related Art
My earlier U.S. Pat. No. 5,020,977 is directed to a compressor for a compression-evaporation cooling system which employs acoustics for compression. The compressor is formed by a standing wave compressor including a chamber for holding a fluid refrigerant. A travelling wave is established in the fluid refrigerant in the chamber. This travelling wave is converted into a standing wave in the fluid refrigerant in the chamber so that the fluid refrigerant is compressed.
Heretofore, the field of linear acoustics was limited primarily to the domain of small acoustic pressure amplitudes. When acoustic pressure amplitudes become large, compared to the average fluid pressure, nonlinearities result. Under these conditions a pure sine wave will normally evolve into a shock wave.
Shock evolution is attributed to a spacial change in sound speed caused by the large variations in pressure, referred to as pressure steepening. During propagation the thermodynamic state of the pressure peak of a finite wave is quite different than its pressure minimum, resulting in different sound speeds along the extent of the wave. Consequently, the pressure peaks of the wave can overtake the pressure minimums and a shock wave evolves.
Shock formation can occur for waves propagating in free space, in wave guides, and in acoustic resonators. The following publications focus on shock formation within various types of acoustic resonators.
Temkin developed a method for calculating the pressure amplitude limit in piston-driven cylindrical resonators, due to shock formation (Samuel Temkin, "Propagating and standing sawtooth waves", J. Acoust. Soc. Am. 45, 224 (1969)). First he assumes the presence of left and right traveling shock waves in a resonator, and then finds the increase in entropy caused by the two shock waves. This entropy loss is substituted into an energy balance equation which is solved for limiting pressure amplitude as a function of driver displacement. Temkin's theory provided close agreement with experimentation for both traveling and standing waves of finite amplitude.
Cruikshank provided a comparison of theory and experiment for finite amplitude acoustic oscillations in piston-driven cylindrical resonators (D. B. Cruikshank, "Experimental investigation of finite-amplitude acoustic oscillations in a closed tube", J. Acoust. Soc. Am. 52, 1024 (1972)). Cruikshank demonstrated close agreement between experimental and theoretically generated shock waveforms.
Like much of the literature, the work of Temkin and Cruikshank both assume piston-driven cylindrical resonators of constant cross-sectional (CCS) area, with the termination of the tube being parallel to the piston face. CCS resonators will have harmonic modes which are coincident in frequency with the wave's harmonics, thus shock evolution is unrestricted. Although not stated in their papers, Temkin and Cruikshank's implicit assumption of a saw-tooth shock wave in their solutions is justified only for CCS resonators.
For resonators with non-harmonic modes, the simple assumption of a sawtooth shock wave will no longer apply. This was shown by Weiner who also developed a method for approximating the limiting pressure amplitude in resonators, due to shock formation (Stephen Weiner, "Standing sound waves of finite amplitude", J. Acoust. Soc. Am. 40, 240 (1966)). Weiner begins by assuming the presence of a shock wave and then calculates the work done on the fundamental by the harmonics. This work is substituted into an energy balance equation which is solved for limiting pressure amplitude as a function of driver displacement.
Weiner then goes on to show that attenuation of the even harmonics will result in a higher pressure amplitude limit for the fundamental. As an example of a resonator that causes even harmonic attenuation, he refers to a T shaped chamber called a "T burner" used for solid-propellent combustion research. The T burner acts as a thermally driven 1/2 wave length resonator with a vent at its center. Each even mode will have a pressure antinode at the vent, and thus experiences attenuation in the form of radiated energy through the vent. Weiner offers no suggestions, other than attenuation, for eliminating harmonics. Attenuation is the dissipation of energy, and thus is undesirable for energy efficiency.
Further examples of harmonic attenuation schemes can be found in the literature of gas-combustion heating. (see for example, Abbot A. Putnam, Combustion-Driven Oscillations in Industry (American Elsevier Publishing Co., 1971)). Other examples can be found in the general field of noise control where attenuation-type schemes are also employed, since energy losses are of no importance. One notably different approach is the work of Oberst, who sought to generate intense sound for calibrating microphones (Hermann Oberst, "A method for the production of extremely powerful standing sound waves in air", Akust. Z. 5, 27 (1940)). Oberst found that the harmonic content of a finite amplitude wave was reduced by a resonator which had non-harmonic resonant modes. His resonator was formed by connecting two tubes of different diameter, with the smaller tube being terminated and the larger tube remaining open. The open end of the resonator was driven by an air jet which was modulated by a rotating aperture disk.
With this arrangement, Oberst was able to produce resonant pressure amplitudes up to 0.10 bar for a driving pressure amplitude of 0.02 bar, giving a gain of 5 to the fundamental. The driving waveform, which had a 30% error (i.e. deviation from a sinusoid), was transformed to a waveform of only 5% error by the resonator. However, he predicted that if more acoustic power were applied, then nonlinear distortions would become clearly evident. In fact, harmonic content is visually noticeable in Oberst's waveforms corresponding to resonant pressure amplitudes of only 0.005 bar.
Oberst attributed the behavior of these finite amplitude waves, to the noncoincidence of the resonator modes and the wave harmonics. Yet, no explanations were offered as to the exact interaction between the resonator and the wave harmonics. Oberst's position seems to be that the reduced spectral density of the resonant wave is simply the result of comparatively little Q-amplification being imparted to the driving waveform harmonics. This explanation is only believable for the modest pressure amplitudes obtained by Oberst. Oberst provided no teachings or suggestions that his methods could produce linear pressure amplitudes above those which he achieved, and he offered no hope for further optimization. To the contrary, Oberst stated that nonlinearities would dominate at higher pressure amplitudes.
A further source of nonlinearity in acoustic resonators is the boundary layer turbulence which can occur at high acoustic velocities. Merkli and Thomann showed experimentally that at finite pressure amplitudes, there is a critical point at which the oscillating laminar flow will become turbulent (P. Merkli, H. Thomann, "Transition to turbulence in oscillating pipe flow", J. Fluid Mech., 68, 567 (1975)). Their studies were also carried out in CCS resonators.
Taken as a whole, the literature of finite resonant acoustics seems to predict that the inherent nonlinearites of fluids will ultimately dominate any resonant system, independent of the boundary conditions imposed by a resonator. The literature's prediction of these limits is far below the actual performance of the present invention.
Therefore, there is a need in the art to efficiently generate very large shock-free acoustic pressure amplitudes as a means of gas compression for vapor-compression heat transfer systems of the type disclosed in my U.S. Pat. No. 5,020,977. Further, many other applications within the field of acoustics, such as thermoacoustic heat engines, can also benefit from the generation of high amplitude sinusoidal waveforms.